Generally, a solenoid converts energy to linear motion. This linear motion may serve many purposes, including but not limited to operation of a mechanical switch and selective control of one or more fluid paths. Solenoid-based systems exhibit varying degrees of efficiency (force per unit of supplied energy), linearity (i.e., of the efficiency curve), proportionality (i.e., of movement to supplied energy), and hysteresis effects (which result in different system response depending on whether the supplied energy is increasing or decreasing). Depending upon their intended use, a solenoid and the system in which it is employed are typically designed to maximize one or more of these characteristics. However, designers face challenges in maximizing one or more of these characteristics while keeping others within desired tolerances.